Ratio word problems and proportions dealing with word problems.

## If 48 marbles are to be divided between bill and carl in the ratio 3:5 how man y marbles will bill get?

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# 5 Answers

Another way to approach this question would be to consider how many equal parts are being distrubed. Looking at the ratio of 3:5 as "for every 3 marbles that Bill gets, Carl get 5," it is easier understand that the marbles will be split into 8 equal parts.

The total marbles: 48 ;

divided by the number of equal parts: 8

gives you 8 groups of 6 marble.

If Bill gets 3 of the groups (each having 6 marbles)

he has a total of 6*3 marbles or 18 marbles.

Bill gets 3/(3+5) of the total.

(3/8)48 = 18

Answer: Bill gets 18 marbles.

Hi Milton;

(3+5)x=48

x=one unit of marbles...

3x+5x=48

8x=48

x=6

3x=3(6)=18=Bill's share

5x=5(6)=30=Carl's share

other approaches

the ratio is 3 to 5

Bill gets 3 marbles for every 8 there are

there are 48 marbles

48/8=6

6x3=18 marbles

(3x)/(5x) for some x simplifies to 3/5 and 3x+5x=48

8x=48

x=6

3*6=18 and 5*6=30

18/30 obviously simplifies to 3/5

the ratio is # of Bill's marbles/# of Carl's marbles, so Bill gets 18 marbles

This is a good problem to use ratio/proportion but we have to make sure we use the correct ratio when solving. The ratio we are given is 3:5 but that is Bill:Carl. We are also given the total so our ratio should be set up as Bills Marbles:Total Marbles.
That would be 3:8. We know that the total marbles is 48. The unknown is Bill's marbles (x).

So since the ratios have to be the same we know that x:48 = 3:8 or x/48 = 3/8.

Cross multiply 8x = 144.

Divide each side by 8. 8x/8 =144/8.

x = 18. Carl gets the other 30. Bill:Carl = 18:30 = 3:5.